Question

In the given figure, $XY\parallel BC$. Find the length of XY, given BC = 6 cm

Answer 1

Given: XY || BC

To find: XY

Since, XY || BC, AB is transversal, then,

$\Delta AXY=\Delta ABC$ [by corresponding angles] Since, XY || BC, AC is transversal, then,

$\Delta AYX=\Delta ABC$ [by corresponding angles] In $\Delta AXY$ and $\Delta$ABC

$\angle AXY=\angle ABC$

$\angle AYX=\angle ACB$

$\Delta$ AXY a $\Delta$ ABC [by AA similarity] Since, triangles are similar, hence corresponding sides will be proportional.

$\therefore \frac{AX}{AB}=\frac{XY}{BC}=\frac{AY}{AC}$

$XY=\frac{6}{4}$

XY = 1.5cm